Weakly interacting light pseudo-scalars are well-motivated in particle
physics. For example, experimental observations require the size of
\(CP\)  violation in strong interactions, parametrized by the angle
\(\theta \) , to be quite small: \(\theta \lesssim 10^{-10}\) . However, the
symmetries of the Standard Model (SM) allow \(\theta \sim 1\) ; this is
the strong \(CP\)  problem. An elegant solution to this puzzle was
proposed by Peccei and Quinn (PQ) [1]}, [2]},
where a new \(U(1)\)  symmetry, anomalous under strong interactions, was
proposed. This \(U(1)\)  symmetry is assumed to be spontaneously broken
at a scale \(f_a\) , resulting in a pseudo-scalar Goldstone boson \(a\) 
[3]}, [4]}, the axion. Non-perturbative
QCD interactions at the scale \(\Lambda _{\rm QCD} \sim 100\,\mathrm {MeV}\) 
generate a potential and hence a mass \(m_a^{PQ} \sim \Lambda _{\rm QCD}^2/f_a\)  for the axion. Experimental and observational bounds
have pushed \(f_a\)  to scales of order \(10^7\,\mathrm {GeV}\)  or more. As
\(f_a\)  sets the inverse coupling of the axion to the SM fields, the
current data suggests that axions are basically `invisible' and very
light. Here we note that some cosmological considerations related to
the overclosure of the universe suggest an upper bound \(f_a \lesssim 10^{12}\)  GeV for the PQ
axion [5]}, [6]}, [7]}, [8]}.
Apart from the considerations related to the strong \(CP\)  problem,
axion-like particles are ubiquitous in string theory. In addition,
axion-like particles have been used in various astrophysical and
cosmological
modelsSee, for
example, Ref. [9]}..
In the following, the term axion is generically used to refer to any of the
above, or other, possible instances of such weakly interacting light
pseudo-scalars.
